1. Chapter 1 Class 9 Number Systems
  2. Concept wise
  3. Rationalising
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If a = 5 + 2√6 and b = 1/a, then what will be the value of a^2+b^2 ?

Last updated at Dec. 16, 2024 by Teachoo

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If a = 5 + 2√6 and b = 1/𝑎, then what will be the value of 𝑎^2+𝑏^2 ? a = 5 + 2√6 b = 1/𝑎 = 1/(5 + 2√6) = 1/(5 + 2√6) × (5 − 2√6)/(5 − 2√6) = (5 − 2√6)/(5^2 − (2√6)^2 ) = (5 − 2√6)/(25 − 24) We know that 〖(𝑎+𝑏)〗^2 = 𝑎^2+𝑏^2+ 2𝑎𝑏 𝒂^𝟐+𝒃^𝟐 = 〖(𝒂+𝒃)〗^𝟐 − 𝟐𝒂𝒃 Here, 𝒂+𝒃 = (5+2√6)+5(5−2√6) 𝒂𝒃 = (5+2√6) (5−2√6) Thus, 𝑎^2+𝑏^2 = 〖(𝑎+𝑏)〗^2 − 2𝑎𝑏 𝑎^2+𝑏^2=〖10〗^2−2 × 1 =100−2 =𝟗𝟖
  1. Chapter 1 Class 9 Number Systems
  2. Concept wise

    3. Rationalising

    Laws of exponents →
Laws of exponents →
Chapter 1 Class 9 Number Systems
Concept wise

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo